A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling

As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling tempor...

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Autores principales:	Hao Li, Enze Zhang
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	optimal experimental design D-optimal design sampling time microalgae growth models Hydraulic engineering TC1-978 Water supply for domestic and industrial purposes TD201-500
Acceso en línea:	https://doaj.org/article/cb5808391f4841e09cc5e4dd014a2690
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spelling	oai:doaj.org-article:cb5808391f4841e09cc5e4dd014a26902021-11-11T19:53:57ZA Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling10.3390/w132129962073-4441https://doaj.org/article/cb5808391f4841e09cc5e4dd014a26902021-10-01T00:00:00Zhttps://www.mdpi.com/2073-4441/13/21/2996https://doaj.org/toc/2073-4441As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. <i>Scenedesmus obliquus</i>, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.Hao LiEnze ZhangMDPI AGarticleoptimal experimental designD-optimal designsampling timemicroalgae growth modelsHydraulic engineeringTC1-978Water supply for domestic and industrial purposesTD201-500ENWater, Vol 13, Iss 2996, p 2996 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	optimal experimental design D-optimal design sampling time microalgae growth models Hydraulic engineering TC1-978 Water supply for domestic and industrial purposes TD201-500
spellingShingle	optimal experimental design D-optimal design sampling time microalgae growth models Hydraulic engineering TC1-978 Water supply for domestic and industrial purposes TD201-500 Hao Li Enze Zhang A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling
description	As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. <i>Scenedesmus obliquus</i>, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.
format	article
author	Hao Li Enze Zhang
author_facet	Hao Li Enze Zhang
author_sort	Hao Li
title	A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling
title_short	A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling
title_full	A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling
title_fullStr	A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling
title_full_unstemmed	A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling
title_sort	coupled sampling design for parameter estimation in microalgae growth experiment: maximizing the benefits of uniform and non-uniform sampling
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/cb5808391f4841e09cc5e4dd014a2690
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A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling

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